This invention relates to n-type narrow-gap semiconductors and more particularly to a method for more accurately determining the compensation density of such semiconductors.
Narrow-gap semiconductors such as InSb, HgCdTe, etc., have important applications in electro-optics because of their use as infrared detectors and as laser materials. In order to provide the best quality materials for such devices, it is necessary to characterize the material as to its quality and suitability for use. In order to characterize such materials, it is very important to determine the donor concentration, N.sub.D, and the acceptor concentration, N.sub.A. The compensation density for n-type, material is equal to the acceptor concentration.
For n-type material, the net impurity density, n, where n=N.sub.D -N.sub.A for monovalent defects, can be determined quite easily from Hall measurements. However, there are no known reliable techniques for determining the density of compensating acceptors, N.sub.A, in n-type narrow-gap materials. For wide-gap semiconductors, N.sub.A, can be determined from measurements of n as a function of temperature. As the temperature decreases, thermal excitation of carriers from the donors and acceptors becomes less probable. The decrease in n with decreasing temperature is known as carrier "freezeout". The change in n with temperature permits one to determine the compensation density. However, such carrier "freezeout" does not occur for n-type narrow gap materials where the donor levels are merged with the conduction band.
A method for determining the compensation density in n-type InSb has been suggested previously. This method relies on a theoretical model to calculate the low temperature mobility for a given electron density, n, using the compensation density as a variable parameter. N.sub.A is obtained by comparing measured and calculated values of mobility. However two serious drawbacks make this approach unreliable. (1) The method is not applicable to the important class of ternary (e.g. Hg.sub.1-x Cd.sub.X Te) and quaternary (e.g. [PbSe].sub.1-x [SnTe].sub.x) compounds. For these mixed compounds, the mobility is extremely sensitive to the alloy composition x. Since this parameter is generally not well known, a simple comparison of the measured and calculated mobility is highly inaccurate. (2) Even for simple compounds like InSb the method is unreliable since it is based on a model which neglects important higher-order corrections to the theory. Comparison of the measured low-temperature mobility to the calculated value for a single value of n is unreliable. To be reliable, theory and experiment must be compared over a wide range of values of n. Consequently there is a need for a non-destructive technique for determining the compensation density for n-type narrow-gap semiconductors.
A previous method has been set forth in an article: "Transport Properties of Photo-Excited Carriers in Slightly Compensated Hg.sub.0.785 Cd.sub.0.215 Te." by F. J. Bartoli et al., Solid State Communications, Vol. 25, pp. 963-966, March 1978, and also has been set forth in patent application Ser. No. 011,821 filed Feb. 13, 1979. In this patent application, the method compares measured values of mobility as a function of photo-excited carrier density to theorectical curves which were calculated assuming a spatially uniform carrier distribution. However, it has been found that this method limits the accuracy to which N.sub.A can be determined because the carriers are generated in a thin layer on the surface of the sample, resulting in a non-uniform center distribution. The non-uniform carrier density results from the large linear absorption coefficient (.alpha.=10.sup.3 to 10.sup.5 cm.sup.-1) for photons with energies greater than the energy gap E.sub.g of the semiconductor. A single photon in this energy range has sufficient energy to excite a valence electron into the conduction band. Correction of the data for the non-uniform carrier distribution must be accomplished using approximate methods, hence introducing error in the technique.